LMFDB - Embedded newform 3420.2.bj.c.1189.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3420,2,Mod(1189,3420)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3420, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 3, 4]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("3420.1189");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3420 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3420.bj (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$27.3088374913$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 20 x^{18} + 261 x^{16} - 1994 x^{14} + 11074 x^{12} - 39211 x^{10} + 99376 x^{8} - 134299 x^{6} + \cdots + 4096 $ x^20 - 20x^18 + 261x^16 - 1994x^14 + 11074x^12 - 39211x^10 + 99376x^8 - 134299x^6 + 124617x^4 - 24768*x^2 + 4096
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 380)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1189.6
Root			$1.74361 + 1.00667i$ of defining polynomial
Character	$\chi$	$=$	3420.1189
Dual form			3420.2.bj.c.2629.6

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0408382 - 2.23570i) q^{5} -1.34403i q^{7} -5.25594 q^{11} +(-2.10918 + 1.21773i) q^{13} +(-1.17765 - 0.679914i) q^{17} +(2.89815 + 3.25587i) q^{19} +(7.05514 - 4.07329i) q^{23} +(-4.99666 + 0.182603i) q^{25} +(1.03597 + 1.79435i) q^{29} -0.513207 q^{31} +(-3.00483 + 0.0548876i) q^{35} -5.57175i q^{37} +(-2.70353 + 4.68265i) q^{41} +(-11.0197 - 6.36221i) q^{43} +(-2.82785 + 1.63266i) q^{47} +5.19359 q^{49} +(-10.1892 + 5.88276i) q^{53} +(0.214643 + 11.7507i) q^{55} +(-0.0175979 + 0.0304805i) q^{59} +(0.518372 + 0.897846i) q^{61} +(2.80861 + 4.66574i) q^{65} +(0.664028 - 0.383377i) q^{67} +(-5.68450 + 9.84583i) q^{71} +(-1.86429 - 1.07635i) q^{73} +7.06413i q^{77} +(-6.48576 + 11.2337i) q^{79} +4.20304i q^{83} +(-1.47199 + 2.66062i) q^{85} +(3.65426 + 6.32937i) q^{89} +(1.63667 + 2.83479i) q^{91} +(7.16079 - 6.61235i) q^{95} +(0.721716 + 0.416683i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - q^{5} + 14 q^{19} + 9 q^{25} + 16 q^{29} + 8 q^{31} + 2 q^{35} - 26 q^{41} - 44 q^{49} - 12 q^{55} - 4 q^{59} + 2 q^{61} + 18 q^{65} + 2 q^{71} - 16 q^{79} - 39 q^{85} + 40 q^{89} - 4 q^{91} + 43 q^{95}+O(q^{100}) $ 20 * q - q^5 + 14 * q^19 + 9 * q^25 + 16 * q^29 + 8 * q^31 + 2 * q^35 - 26 * q^41 - 44 * q^49 - 12 * q^55 - 4 * q^59 + 2 * q^61 + 18 * q^65 + 2 * q^71 - 16 * q^79 - 39 * q^85 + 40 * q^89 - 4 * q^91 + 43 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3420\mathbb{Z}\right)^\times$.

$n$	$1711$	$1901$	$2737$	$3061$
$\chi(n)$	$1$	$1$	$-1$	$e\left(\frac{2}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	−0.0408382	−	2.23570i	−0.0182634	−	0.999833i
$5$	−0.0408382	−	2.23570i	−0.0182634	−	0.999833i
$6$		0			0
$7$		−	1.34403i		−	0.507994i	−0.967205	−	0.253997i	$-0.918255\pi$
$7$		−	1.34403i		−	0.507994i	0.967205	−	0.253997i	$-0.0817454\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−5.25594			−1.58473			−0.792363	−	0.610050i	$-0.791149\pi$
$11$	−5.25594			−1.58473			−0.792363	+	0.610050i	$0.791149\pi$
$12$		0			0
$13$	−2.10918	+	1.21773i	−0.584980	+	0.337738i	−0.763110	−	0.646269i	$-0.776329\pi$
$13$	−2.10918	+	1.21773i	−0.584980	+	0.337738i	0.178130	+	0.984007i	$0.442995\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−1.17765	−	0.679914i	−0.285621	−	0.164903i	0.350344	−	0.936621i	$-0.386065\pi$
$17$	−1.17765	−	0.679914i	−0.285621	−	0.164903i	−0.635965	+	0.771718i	$0.719398\pi$
$18$		0			0
$19$	2.89815	+	3.25587i	0.664882	+	0.746949i
$19$	2.89815	+	3.25587i	0.664882	+	0.746949i
$20$		0			0
$21$		0			0
$22$		0			0
$23$	7.05514	−	4.07329i	1.47110	−	0.849339i	0.471625	−	0.881799i	$-0.343668\pi$
$23$	7.05514	−	4.07329i	1.47110	−	0.849339i	0.999473	+	0.0324603i	$0.0103342\pi$
$24$		0			0
$25$	−4.99666	+	0.182603i	−0.999333	+	0.0365207i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	1.03597	+	1.79435i	0.192375	+	0.333203i	0.946037	−	0.324059i	$-0.105048\pi$
$29$	1.03597	+	1.79435i	0.192375	+	0.333203i	−0.753662	+	0.657262i	$0.771714\pi$
$30$		0			0
$31$	−0.513207			−0.0921747			−0.0460873	−	0.998937i	$-0.514675\pi$
$31$	−0.513207			−0.0921747			−0.0460873	+	0.998937i	$0.514675\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−3.00483	+	0.0548876i	−0.507910	+	0.00927770i
$36$		0			0
$37$		−	5.57175i		−	0.915991i	−0.888955	−	0.457995i	$-0.848568\pi$
$37$		−	5.57175i		−	0.915991i	0.888955	−	0.457995i	$-0.151432\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−2.70353	+	4.68265i	−0.422220	+	0.731307i	−0.996156	−	0.0875933i	$-0.972082\pi$
$41$	−2.70353	+	4.68265i	−0.422220	+	0.731307i	0.573936	+	0.818900i	$0.305416\pi$
$42$		0			0
$43$	−11.0197	−	6.36221i	−1.68048	−	0.970228i	−0.961339	−	0.275369i	$-0.911200\pi$
$43$	−11.0197	−	6.36221i	−1.68048	−	0.970228i	−0.719146	−	0.694859i	$-0.755467\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−2.82785	+	1.63266i	−0.412485	+	0.238148i	−0.691857	−	0.722035i	$-0.743207\pi$
$47$	−2.82785	+	1.63266i	−0.412485	+	0.238148i	0.279372	+	0.960183i	$0.409874\pi$
$48$		0			0
$49$	5.19359			0.741942
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−10.1892	+	5.88276i	−1.39960	+	0.808060i	−0.994351	−	0.106146i	$-0.966149\pi$
$53$	−10.1892	+	5.88276i	−1.39960	+	0.808060i	−0.405250	+	0.914206i	$0.632815\pi$
$54$		0			0
$55$	0.214643	+	11.7507i	0.0289425	+	1.58446i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−0.0175979	+	0.0304805i	−0.00229105	+	0.00396822i	−0.867169	−	0.498015i	$-0.834063\pi$
$59$	−0.0175979	+	0.0304805i	−0.00229105	+	0.00396822i	0.864878	+	0.501983i	$0.167396\pi$
$60$		0			0
$61$	0.518372	+	0.897846i	0.0663707	+	0.114957i	0.897301	−	0.441419i	$-0.145525\pi$
$61$	0.518372	+	0.897846i	0.0663707	+	0.114957i	−0.830930	+	0.556376i	$0.812191\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	2.80861	+	4.66574i	0.348366	+	0.578714i
$66$		0			0
$67$	0.664028	−	0.383377i	0.0811239	−	0.0468369i	−0.458889	−	0.888493i	$-0.651753\pi$
$67$	0.664028	−	0.383377i	0.0811239	−	0.0468369i	0.540013	+	0.841657i	$0.318419\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−5.68450	+	9.84583i	−0.674625	+	1.16849i	0.301953	+	0.953323i	$0.402362\pi$
$71$	−5.68450	+	9.84583i	−0.674625	+	1.16849i	−0.976578	+	0.215163i	$0.930972\pi$
$72$		0			0
$73$	−1.86429	−	1.07635i	−0.218199	−	0.125977i	0.386917	−	0.922115i	$-0.373540\pi$
$73$	−1.86429	−	1.07635i	−0.218199	−	0.125977i	−0.605116	+	0.796137i	$0.706873\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$			7.06413i			0.805032i
$78$		0			0
$79$	−6.48576	+	11.2337i	−0.729705	+	1.26389i	0.227302	+	0.973824i	$0.427009\pi$
$79$	−6.48576	+	11.2337i	−0.729705	+	1.26389i	−0.957008	+	0.290062i	$0.906324\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$			4.20304i			0.461343i	0.973032	+	0.230672i	$0.0740923\pi$
$83$			4.20304i			0.461343i	−0.973032	+	0.230672i	$0.925908\pi$
$84$		0			0
$85$	−1.47199	+	2.66062i	−0.159660	+	0.288585i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	3.65426	+	6.32937i	0.387351	+	0.670912i	0.992092	−	0.125510i	$-0.0400568\pi$
$89$	3.65426	+	6.32937i	0.387351	+	0.670912i	−0.604741	+	0.796422i	$0.706723\pi$
$90$		0			0
$91$	1.63667	+	2.83479i	0.171569	+	0.297166i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	7.16079	−	6.61235i	0.734681	−	0.678413i
$96$		0			0
$97$	0.721716	+	0.416683i	0.0732791	+	0.0423077i	0.536192	−	0.844096i	$-0.319862\pi$
$97$	0.721716	+	0.416683i	0.0732791	+	0.0423077i	−0.462913	+	0.886404i	$0.653196\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	7.40992	+	12.8344i	0.737315	+	1.27707i	0.953700	+	0.300759i	$0.0972400\pi$
$101$	7.40992	+	12.8344i	0.737315	+	1.27707i	−0.216385	+	0.976308i	$0.569427\pi$
$102$		0			0
$103$			9.40773i			0.926971i	0.886104	+	0.463486i	$0.153401\pi$
$103$			9.40773i			0.926971i	−0.886104	+	0.463486i	$0.846599\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$		−	12.8130i		−	1.23868i	−0.785124	−	0.619338i	$-0.787401\pi$
$107$		−	12.8130i		−	1.23868i	0.785124	−	0.619338i	$-0.212599\pi$
$108$		0			0
$109$	0.996875	−	1.72664i	0.0954833	−	0.165382i	−0.814327	−	0.580406i	$-0.802894\pi$
$109$	0.996875	−	1.72664i	0.0954833	−	0.165382i	0.909810	+	0.415025i	$0.136227\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$			8.34647i			0.785170i	0.919716	+	0.392585i	$0.128419\pi$
$113$			8.34647i			0.785170i	−0.919716	+	0.392585i	$0.871581\pi$
$114$		0			0
$115$	−9.39474	−	15.6068i	−0.876064	−	1.45534i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−0.913823	+	1.58279i	−0.0837700	+	0.145094i
$120$		0			0
$121$	16.6249			1.51136
$122$		0			0
$123$		0			0
$124$		0			0
$125$	0.612300	+	11.1636i	0.0547658	+	0.998499i
$126$		0			0
$127$	−17.8240	+	10.2907i	−1.58163	+	0.913153i	−0.587005	+	0.809583i	$0.699693\pi$
$127$	−17.8240	+	10.2907i	−1.58163	+	0.913153i	−0.994622	+	0.103569i	$0.966974\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	5.36554	−	9.29339i	0.468790	−	0.811967i	−0.530574	−	0.847639i	$-0.678024\pi$
$131$	5.36554	−	9.29339i	0.468790	−	0.811967i	0.999364	+	0.0356712i	$0.0113569\pi$
$132$		0			0
$133$	4.37598	−	3.89519i	0.379446	−	0.337756i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	14.8771	−	8.58931i	1.27104	−	0.733834i	0.295855	−	0.955233i	$-0.404396\pi$
$137$	14.8771	−	8.58931i	1.27104	−	0.733834i	0.975183	+	0.221399i	$0.0710622\pi$
$138$		0			0
$139$	3.66394	+	6.34613i	0.310771	+	0.538272i	0.978530	−	0.206106i	$-0.0660793\pi$
$139$	3.66394	+	6.34613i	0.310771	+	0.538272i	−0.667758	+	0.744378i	$0.732746\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	11.0857	−	6.40033i	0.927033	−	0.535223i
$144$		0			0
$145$	3.96932	−	2.38939i	0.329634	−	0.198428i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	6.12292	−	10.6052i	0.501609	−	0.868812i	−0.498389	−	0.866953i	$-0.666075\pi$
$149$	6.12292	−	10.6052i	0.501609	−	0.868812i	0.999998	−	0.00185904i	$-0.000591751\pi$
$150$		0			0
$151$	−11.5577			−0.940549			−0.470274	−	0.882520i	$-0.655845\pi$
$151$	−11.5577			−0.940549			−0.470274	+	0.882520i	$0.655845\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	0.0209584	+	1.14737i	0.00168342	+	0.0921593i
$156$		0			0
$157$	3.58528	+	2.06996i	0.286137	+	0.165201i	0.636198	−	0.771526i	$-0.280506\pi$
$157$	3.58528	+	2.06996i	0.286137	+	0.165201i	−0.350062	+	0.936727i	$0.613839\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−5.47460	−	9.48229i	−0.431459	−	0.747309i
$162$		0			0
$163$			9.41672i			0.737575i	0.929514	+	0.368787i	$0.120227\pi$
$163$			9.41672i			0.737575i	−0.929514	+	0.368787i	$0.879773\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−11.8395	+	6.83551i	−0.916164	+	0.528948i	−0.882409	−	0.470482i	$-0.844080\pi$
$167$	−11.8395	+	6.83551i	−0.916164	+	0.528948i	−0.0337550	+	0.999430i	$0.510747\pi$
$168$		0			0
$169$	−3.53425	+	6.12151i	−0.271866	+	0.470885i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	10.1999	+	5.88891i	0.775484	+	0.447726i	0.834827	−	0.550512i	$-0.185567\pi$
$173$	10.1999	+	5.88891i	0.775484	+	0.447726i	−0.0593437	+	0.998238i	$0.518901\pi$
$174$		0			0
$175$	0.245424	+	6.71565i	0.0185523	+	0.507655i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−16.5727			−1.23870			−0.619350	−	0.785115i	$-0.712604\pi$
$179$	−16.5727			−1.23870			−0.619350	+	0.785115i	$0.712604\pi$
$180$		0			0
$181$	7.19552	+	12.4630i	0.534839	+	0.926368i	0.999171	+	0.0407069i	$0.0129610\pi$
$181$	7.19552	+	12.4630i	0.534839	+	0.926368i	−0.464332	+	0.885661i	$0.653706\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−12.4567	+	0.227540i	−0.915838	+	0.0167291i
$186$		0			0
$187$	6.18964	+	3.57359i	0.452631	+	0.261327i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	5.97170			0.432097			0.216049	−	0.976383i	$-0.430683\pi$
$191$	5.97170			0.432097			0.216049	+	0.976383i	$0.430683\pi$
$192$		0			0
$193$	14.1046	+	8.14331i	1.01527	+	0.586168i	0.912731	−	0.408560i	$-0.133969\pi$
$193$	14.1046	+	8.14331i	1.01527	+	0.586168i	0.102542	+	0.994729i	$0.467302\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$		−	11.5233i		−	0.820998i	−0.911861	−	0.410499i	$-0.865355\pi$
$197$		−	11.5233i		−	0.820998i	0.911861	−	0.410499i	$-0.134645\pi$
$198$		0			0
$199$	4.79943	+	8.31285i	0.340222	+	0.589283i	0.984474	−	0.175531i	$-0.0561643\pi$
$199$	4.79943	+	8.31285i	0.340222	+	0.589283i	−0.644251	+	0.764814i	$0.722831\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	2.41166	−	1.39237i	0.169265	−	0.0977253i
$204$		0			0
$205$	10.5794	+	5.85303i	0.738896	+	0.408794i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−15.2325	−	17.1127i	−1.05366	−	1.18371i
$210$		0			0
$211$	7.28207	−	12.6129i	0.501318	−	0.868308i	−0.498681	−	0.866786i	$-0.666182\pi$
$211$	7.28207	−	12.6129i	0.501318	−	0.868308i	0.999999	−	0.00152265i	$-0.000484675\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−13.7739	+	24.8964i	−0.939375	+	1.69792i
$216$		0			0
$217$			0.689764i			0.0468242i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	3.31182			0.222777
$222$		0			0
$223$	−6.55816	−	3.78635i	−0.439167	−	0.253553i	0.264077	−	0.964501i	$-0.414933\pi$
$223$	−6.55816	−	3.78635i	−0.439167	−	0.253553i	−0.703244	+	0.710949i	$0.748266\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$		−	6.86640i		−	0.455739i	−0.973692	−	0.227869i	$-0.926824\pi$
$227$		−	6.86640i		−	0.455739i	0.973692	−	0.227869i	$-0.0731759\pi$
$228$		0			0
$229$	−22.1011			−1.46048			−0.730240	−	0.683191i	$-0.760592\pi$
$229$	−22.1011			−1.46048			−0.730240	+	0.683191i	$0.760592\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−2.57806	−	1.48844i	−0.168894	−	0.0975111i	0.413170	−	0.910654i	$-0.364421\pi$
$233$	−2.57806	−	1.48844i	−0.168894	−	0.0975111i	−0.582064	+	0.813143i	$0.697755\pi$
$234$		0			0
$235$	3.76562	+	6.25555i	0.245642	+	0.408067i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−9.71289			−0.628275			−0.314137	−	0.949378i	$-0.601715\pi$
$239$	−9.71289			−0.628275			−0.314137	+	0.949378i	$0.601715\pi$
$240$		0			0
$241$	9.34287	+	16.1823i	0.601827	+	1.04239i	0.992544	+	0.121884i	$0.0388937\pi$
$241$	9.34287	+	16.1823i	0.601827	+	1.04239i	−0.390717	+	0.920511i	$0.627773\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−0.212097	−	11.6113i	−0.0135504	−	0.741818i
$246$		0			0
$247$	−10.0775	−	3.33803i	−0.641216	−	0.212394i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−2.10091	−	3.63888i	−0.132608	−	0.229684i	0.792073	−	0.610426i	$-0.209002\pi$
$251$	−2.10091	−	3.63888i	−0.132608	−	0.229684i	−0.924681	+	0.380742i	$0.875668\pi$
$252$		0			0
$253$	−37.0814	+	21.4090i	−2.33129	+	1.34597i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−24.3946	+	14.0842i	−1.52169	+	0.878548i	−0.522018	+	0.852934i	$0.674821\pi$
$257$	−24.3946	+	14.0842i	−1.52169	+	0.878548i	−0.999672	+	0.0256140i	$0.991846\pi$
$258$		0			0
$259$	−7.48859			−0.465318
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−2.34563	−	1.35425i	−0.144637	−	0.0835065i	0.425935	−	0.904754i	$-0.359945\pi$
$263$	−2.34563	−	1.35425i	−0.144637	−	0.0835065i	−0.570572	+	0.821247i	$0.693279\pi$
$264$		0			0
$265$	13.5682	+	22.5398i	0.833486	+	1.38461i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−5.64101	+	9.77052i	−0.343938	+	0.595719i	−0.985160	−	0.171637i	$-0.945094\pi$
$269$	−5.64101	+	9.77052i	−0.343938	+	0.595719i	0.641222	+	0.767356i	$0.278428\pi$
$270$		0			0
$271$	−3.16690	+	5.48523i	−0.192375	+	0.333204i	−0.946037	−	0.324059i	$-0.894952\pi$
$271$	−3.16690	+	5.48523i	−0.192375	+	0.333204i	0.753662	+	0.657263i	$0.228286\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	26.2622	−	0.959753i	1.58367	−	0.0578753i
$276$		0			0
$277$		−	11.1435i		−	0.669549i	−0.942298	−	0.334774i	$-0.891340\pi$
$277$		−	11.1435i		−	0.669549i	0.942298	−	0.334774i	$-0.108660\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	12.9061	+	22.3541i	0.769916	+	1.33353i	0.937608	+	0.347694i	$0.113035\pi$
$281$	12.9061	+	22.3541i	0.769916	+	1.33353i	−0.167693	+	0.985839i	$0.553632\pi$
$282$		0			0
$283$	−24.9942	−	14.4304i	−1.48575	−	0.857799i	−0.485883	−	0.874024i	$-0.661502\pi$
$283$	−24.9942	−	14.4304i	−1.48575	−	0.857799i	−0.999868	+	0.0162249i	$0.994835\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	6.29360	+	3.63361i	0.371500	+	0.214485i
$288$		0			0
$289$	−7.57543	−	13.1210i	−0.445614	−	0.771826i
$290$		0			0
$291$		0			0
$292$		0			0
$293$		−	22.7742i		−	1.33048i	−0.746628	−	0.665242i	$-0.768328\pi$
$293$		−	22.7742i		−	1.33048i	0.746628	−	0.665242i	$-0.231672\pi$
$294$		0			0
$295$	0.0688637	+	0.0380988i	0.00400940	+	0.00221820i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−9.92035	+	17.1825i	−0.573709	+	0.993692i
$300$		0			0
$301$	−8.55098	+	14.8107i	−0.492870	+	0.853676i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	1.98614	−	1.19559i	0.113726	−	0.0684592i
$306$		0			0
$307$	14.0275	+	8.09880i	0.800593	+	0.462223i	0.843679	−	0.536849i	$-0.180385\pi$
$307$	14.0275	+	8.09880i	0.800593	+	0.462223i	−0.0430854	+	0.999071i	$0.513719\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	28.3483			1.60749			0.803743	−	0.594977i	$-0.202839\pi$
$311$	28.3483			1.60749			0.803743	+	0.594977i	$0.202839\pi$
$312$		0			0
$313$	2.67539	−	1.54464i	0.151222	−	0.0873081i	−0.422480	−	0.906372i	$-0.638840\pi$
$313$	2.67539	−	1.54464i	0.151222	−	0.0873081i	0.573702	+	0.819064i	$0.305507\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−20.8236	+	12.0225i	−1.16957	+	0.675251i	−0.953579	−	0.301144i	$-0.902632\pi$
$317$	−20.8236	+	12.0225i	−1.16957	+	0.675251i	−0.215991	+	0.976395i	$0.569298\pi$
$318$		0			0
$319$	−5.44500	−	9.43101i	−0.304861	−	0.528035i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−1.19928	−	5.80476i	−0.0667298	−	0.322986i
$324$		0			0
$325$	10.3165	−	6.46975i	0.572255	−	0.358877i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	2.19434	+	3.80071i	0.120978	+	0.209540i
$330$		0			0
$331$	−20.7717			−1.14171			−0.570857	−	0.821049i	$-0.693389\pi$
$331$	−20.7717			−1.14171			−0.570857	+	0.821049i	$0.693389\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−0.884231	−	1.46891i	−0.0483107	−	0.0802550i
$336$		0			0
$337$	−2.10139	−	1.21324i	−0.114470	−	0.0660892i	0.441672	−	0.897177i	$-0.354386\pi$
$337$	−2.10139	−	1.21324i	−0.114470	−	0.0660892i	−0.556142	+	0.831087i	$0.687719\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	2.69739			0.146072
$342$		0			0
$343$		−	16.3885i		−	0.884896i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−2.48834	−	1.43664i	−0.133581	−	0.0771230i	0.431720	−	0.902008i	$-0.357907\pi$
$347$	−2.48834	−	1.43664i	−0.133581	−	0.0771230i	−0.565301	+	0.824885i	$0.691240\pi$
$348$		0			0
$349$	5.89385			0.315490			0.157745	−	0.987480i	$-0.449578\pi$
$349$	5.89385			0.315490			0.157745	+	0.987480i	$0.449578\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$		−	12.0238i		−	0.639962i	−0.947424	−	0.319981i	$-0.896324\pi$
$353$		−	12.0238i		−	0.639962i	0.947424	−	0.319981i	$-0.103676\pi$
$354$		0			0
$355$	22.2444	+	12.3067i	1.18061	+	0.653172i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	2.26590	−	3.92466i	0.119590	−	0.207136i	−0.800015	−	0.599979i	$-0.795175\pi$
$359$	2.26590	−	3.92466i	0.119590	−	0.207136i	0.919605	+	0.392844i	$0.128509\pi$
$360$		0			0
$361$	−2.20143	+	18.8720i	−0.115865	+	0.993265i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−2.33026	+	4.21195i	−0.121971	+	0.220463i
$366$		0			0
$367$	29.9143	−	17.2710i	1.56151	−	0.901539i	0.564407	−	0.825496i	$-0.309105\pi$
$367$	29.9143	−	17.2710i	1.56151	−	0.901539i	0.997105	−	0.0760429i	$-0.0242286\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	7.90659	+	13.6946i	0.410490	+	0.710989i
$372$		0			0
$373$		−	24.0801i		−	1.24682i	−0.781894	−	0.623411i	$-0.785746\pi$
$373$		−	24.0801i		−	1.24682i	0.781894	−	0.623411i	$-0.214254\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−4.37008	−	2.52307i	−0.225071	−	0.129945i
$378$		0			0
$379$	−30.1565			−1.54904			−0.774518	−	0.632552i	$-0.782008\pi$
$379$	−30.1565			−1.54904			−0.774518	+	0.632552i	$0.782008\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−33.6192	−	19.4101i	−1.71786	−	0.991809i	−0.922797	−	0.385286i	$-0.874103\pi$
$383$	−33.6192	−	19.4101i	−1.71786	−	0.991809i	−0.795066	−	0.606522i	$-0.792564\pi$
$384$		0			0
$385$	15.7932	−	0.288486i	0.804898	−	0.0147026i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−18.6935	−	32.3781i	−0.947799	−	1.64164i	−0.750048	−	0.661383i	$-0.769970\pi$
$389$	−18.6935	−	32.3781i	−0.947799	−	1.64164i	−0.197750	−	0.980252i	$-0.563364\pi$
$390$		0			0
$391$	−11.0779			−0.560236
$392$		0			0
$393$		0			0
$394$		0			0
$395$	25.3799	+	14.0414i	1.27700	+	0.706501i
$396$		0			0
$397$	−13.4790	−	7.78211i	−0.676492	−	0.390573i	0.122040	−	0.992525i	$-0.461056\pi$
$397$	−13.4790	−	7.78211i	−0.676492	−	0.390573i	−0.798532	+	0.601952i	$0.794390\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	11.3113	−	19.5918i	0.564860	−	0.978366i	−0.432203	−	0.901777i	$-0.642263\pi$
$401$	11.3113	−	19.5918i	0.564860	−	0.978366i	0.997063	−	0.0765898i	$-0.0244032\pi$
$402$		0			0
$403$	1.08244	−	0.624949i	0.0539203	−	0.0311309i
$404$		0			0
$405$		0			0
$406$		0			0
$407$			29.2848i			1.45159i
$408$		0			0
$409$	−18.1239	−	31.3915i	−0.896169	−	1.55221i	−0.832351	−	0.554249i	$-0.813005\pi$
$409$	−18.1239	−	31.3915i	−0.896169	−	1.55221i	−0.0638187	−	0.997962i	$-0.520328\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	0.0409666	+	0.0236521i	0.00201583	+	0.00116384i
$414$		0			0
$415$	9.39671	−	0.171644i	0.461266	−	0.00842569i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−14.5598			−0.711293			−0.355647	−	0.934621i	$-0.615739\pi$
$419$	−14.5598			−0.711293			−0.355647	+	0.934621i	$0.615739\pi$
$420$		0			0
$421$	−0.784161	+	1.35821i	−0.0382177	+	0.0661950i	−0.884502	−	0.466537i	$-0.845501\pi$
$421$	−0.784161	+	1.35821i	−0.0382177	+	0.0661950i	0.846284	+	0.532732i	$0.178835\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	6.00846	+	3.18226i	0.291453	+	0.154362i
$426$		0			0
$427$	1.20673	−	0.696705i	0.0583977	−	0.0337159i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−12.7303	−	22.0495i	−0.613197	−	1.06209i	−0.990698	−	0.136080i	$-0.956550\pi$
$431$	−12.7303	−	22.0495i	−0.613197	−	1.06209i	0.377500	−	0.926009i	$-0.376784\pi$
$432$		0			0
$433$	14.6212	−	8.44155i	0.702650	−	0.405675i	−0.105684	−	0.994400i	$-0.533703\pi$
$433$	14.6212	−	8.44155i	0.702650	−	0.405675i	0.808334	+	0.588725i	$0.200370\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	33.7090	+	11.1656i	1.61252	+	0.534125i
$438$		0			0
$439$	9.93240	−	17.2034i	0.474048	−	0.821075i	−0.525511	−	0.850787i	$-0.676126\pi$
$439$	9.93240	−	17.2034i	0.474048	−	0.821075i	0.999558	+	0.0297121i	$0.00945905\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−4.46422	+	2.57742i	−0.212101	+	0.122457i	−0.602288	−	0.798279i	$-0.705744\pi$
$443$	−4.46422	+	2.57742i	−0.212101	+	0.122457i	0.390186	+	0.920736i	$0.372411\pi$
$444$		0			0
$445$	14.0013	−	8.42830i	0.663726	−	0.399540i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−33.2207			−1.56778			−0.783892	−	0.620897i	$-0.786768\pi$
$449$	−33.2207			−1.56778			−0.783892	+	0.620897i	$0.786768\pi$
$450$		0			0
$451$	14.2096	−	24.6117i	0.669103	−	1.15892i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	6.27088	−	3.77485i	0.293983	−	0.176968i
$456$		0			0
$457$			11.7126i			0.547894i	0.961745	+	0.273947i	$0.0883293\pi$
$457$			11.7126i			0.547894i	−0.961745	+	0.273947i	$0.911671\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−3.68501	+	6.38263i	−0.171628	+	0.297269i	−0.938989	−	0.343947i	$-0.888236\pi$
$461$	−3.68501	+	6.38263i	−0.171628	+	0.297269i	0.767361	+	0.641215i	$0.221569\pi$
$462$		0			0
$463$			28.8020i			1.33854i	0.743019	+	0.669271i	$0.233393\pi$
$463$			28.8020i			1.33854i	−0.743019	+	0.669271i	$0.766607\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$		−	34.1251i		−	1.57912i	−0.613673	−	0.789561i	$-0.710309\pi$
$467$		−	34.1251i		−	1.57912i	0.613673	−	0.789561i	$-0.289691\pi$
$468$		0			0
$469$	−0.515268	−	0.892471i	−0.0237929	−	0.0412105i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	57.9188	+	33.4394i	2.66311	+	1.53755i
$474$		0			0
$475$	−15.0756	−	15.7393i	−0.691717	−	0.722169i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−14.4130	−	24.9640i	−0.658546	−	1.14064i	−0.980992	−	0.194048i	$-0.937838\pi$
$479$	−14.4130	−	24.9640i	−0.658546	−	1.14064i	0.322446	−	0.946588i	$-0.395495\pi$
$480$		0			0
$481$	6.78491	+	11.7518i	0.309365	+	0.535836i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	0.902102	−	1.63055i	0.0409623	−	0.0740396i
$486$		0			0
$487$			16.5796i			0.751294i	0.926763	+	0.375647i	$0.122579\pi$
$487$			16.5796i			0.751294i	−0.926763	+	0.375647i	$0.877421\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	4.94615	−	8.56698i	0.223217	−	0.386623i	−0.732566	−	0.680696i	$-0.761678\pi$
$491$	4.94615	−	8.56698i	0.223217	−	0.386623i	0.955783	+	0.294073i	$0.0950109\pi$
$492$		0			0
$493$		−	2.81748i		−	0.126893i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	13.2331	+	7.64011i	0.593584	+	0.342706i
$498$		0			0
$499$	−15.4949	+	26.8380i	−0.693649	+	1.20144i	0.276985	+	0.960874i	$0.410665\pi$
$499$	−15.4949	+	26.8380i	−0.693649	+	1.20144i	−0.970634	+	0.240561i	$0.922669\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−11.1406	+	6.43203i	−0.496735	+	0.286790i	−0.727364	−	0.686252i	$-0.759255\pi$
$503$	−11.1406	+	6.43203i	−0.496735	+	0.286790i	0.230629	+	0.973042i	$0.425922\pi$
$504$		0			0
$505$	28.3911	−	17.0905i	1.26339	−	0.760516i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	7.35312	+	12.7360i	0.325921	+	0.564512i	0.981698	−	0.190442i	$-0.0609922\pi$
$509$	7.35312	+	12.7360i	0.325921	+	0.564512i	−0.655777	+	0.754955i	$0.727659\pi$
$510$		0			0
$511$	−1.44664	+	2.50566i	−0.0639957	+	0.110844i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	21.0328	−	0.384195i	0.926817	−	0.0169296i
$516$		0			0
$517$	14.8630	−	8.58118i	0.653676	−	0.377400i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−5.35528			−0.234619			−0.117310	−	0.993095i	$-0.537427\pi$
$521$	−5.35528			−0.234619			−0.117310	+	0.993095i	$0.537427\pi$
$522$		0			0
$523$	−13.8388	+	7.98981i	−0.605127	+	0.349370i	−0.771056	−	0.636768i	$-0.780271\pi$
$523$	−13.8388	+	7.98981i	−0.605127	+	0.349370i	0.165929	+	0.986138i	$0.446938\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	0.604376	+	0.348937i	0.0263270	+	0.0151999i
$528$		0			0
$529$	21.6833	−	37.5566i	0.942753	−	1.63290i
$530$		0			0
$531$		0			0
$532$		0			0
$533$		−	13.1687i		−	0.570400i
$534$		0			0
$535$	−28.6459	+	0.523258i	−1.23847	+	0.0226224i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−27.2972			−1.17577
$540$		0			0
$541$	−17.9500	−	31.0904i	−0.771732	−	1.33668i	−0.936613	−	0.350366i	$-0.886057\pi$
$541$	−17.9500	−	31.0904i	−0.771732	−	1.33668i	0.164881	−	0.986313i	$-0.447276\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−3.90095	−	2.15820i	−0.167098	−	0.0924469i
$546$		0			0
$547$	−22.6473	+	13.0754i	−0.968327	+	0.559064i	−0.898726	−	0.438511i	$-0.855506\pi$
$547$	−22.6473	+	13.0754i	−0.968327	+	0.559064i	−0.0696011	+	0.997575i	$0.522173\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−2.83979	+	8.57329i	−0.120979	+	0.365235i
$552$		0			0
$553$	15.0983	+	8.71704i	0.642047	+	0.370686i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	3.64444	−	2.10412i	0.154420	−	0.0891543i	−0.420799	−	0.907154i	$-0.638250\pi$
$557$	3.64444	−	2.10412i	0.154420	−	0.0891543i	0.575219	+	0.818000i	$0.304917\pi$
$558$		0			0
$559$	30.9899			1.31073
$560$		0			0
$561$		0			0
$562$		0			0
$563$			40.5225i			1.70782i	0.520422	+	0.853909i	$0.325775\pi$
$563$			40.5225i			1.70782i	−0.520422	+	0.853909i	$0.674225\pi$
$564$		0			0
$565$	18.6602	−	0.340855i	0.785039	−	0.0143399i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	23.9522			1.00413			0.502064	−	0.864831i	$-0.332574\pi$
$569$	23.9522			1.00413			0.502064	+	0.864831i	$0.332574\pi$
$570$		0			0
$571$	−7.78949			−0.325980			−0.162990	−	0.986628i	$-0.552114\pi$
$571$	−7.78949			−0.325980			−0.162990	+	0.986628i	$0.552114\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−34.5084	+	21.6411i	−1.43910	+	0.902498i
$576$		0			0
$577$			34.1385i			1.42121i	0.703593	+	0.710603i	$0.251578\pi$
$577$			34.1385i			1.42121i	−0.703593	+	0.710603i	$0.748422\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	5.64899			0.234360
$582$		0			0
$583$	53.5541	−	30.9195i	2.21798	−	1.28055i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−19.1737	−	11.0700i	−0.791384	−	0.456906i	0.0490654	−	0.998796i	$-0.484376\pi$
$587$	−19.1737	−	11.0700i	−0.791384	−	0.456906i	−0.840450	+	0.541890i	$0.817709\pi$
$588$		0			0
$589$	−1.48735	−	1.67094i	−0.0612853	−	0.0688498i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	35.8131	−	20.6767i	1.47067	−	0.849089i	0.471208	−	0.882022i	$-0.343818\pi$
$593$	35.8131	−	20.6767i	1.47067	−	0.849089i	0.999458	+	0.0329325i	$0.0104846\pi$
$594$		0			0
$595$	3.57595	+	1.97839i	0.146600	+	0.0811061i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−16.8243	−	29.1406i	−0.687423	−	1.19065i	−0.972669	−	0.232197i	$-0.925409\pi$
$599$	−16.8243	−	29.1406i	−0.687423	−	1.19065i	0.285246	−	0.958454i	$-0.407925\pi$
$600$		0			0
$601$	38.4939			1.57020			0.785100	−	0.619369i	$-0.212611\pi$
$601$	38.4939			1.57020			0.785100	+	0.619369i	$0.212611\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−0.678932	−	37.1683i	−0.0276025	−	1.51111i
$606$		0			0
$607$		−	22.1827i		−	0.900367i	−0.892936	−	0.450183i	$-0.851359\pi$
$607$		−	22.1827i		−	0.900367i	0.892936	−	0.450183i	$-0.148641\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	3.97629	−	6.88714i	0.160864	−	0.278624i
$612$		0			0
$613$	4.13445	+	2.38703i	0.166989	+	0.0964111i	0.581165	−	0.813786i	$-0.302597\pi$
$613$	4.13445	+	2.38703i	0.166989	+	0.0964111i	−0.414176	+	0.910197i	$0.635930\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	14.0178	−	8.09317i	0.564335	−	0.325819i	−0.190549	−	0.981678i	$-0.561027\pi$
$617$	14.0178	−	8.09317i	0.564335	−	0.325819i	0.754883	+	0.655859i	$0.227693\pi$
$618$		0			0
$619$	−13.4892			−0.542176			−0.271088	−	0.962555i	$-0.587383\pi$
$619$	−13.4892			−0.542176			−0.271088	+	0.962555i	$0.587383\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	8.50684	−	4.91143i	0.340819	−	0.196772i
$624$		0			0
$625$	24.9333	−	1.82482i	0.997332	−	0.0729926i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−3.78832	+	6.56156i	−0.151050	+	0.261626i
$630$		0			0
$631$	13.2207	+	22.8989i	0.526308	+	0.911592i	0.999530	+	0.0306488i	$0.00975735\pi$
$631$	13.2207	+	22.8989i	0.526308	+	0.911592i	−0.473222	+	0.880943i	$0.656909\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	23.7348	+	39.4288i	0.941886	+	1.56469i
$636$		0			0
$637$	−10.9542	+	6.32441i	−0.434021	+	0.250582i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	4.27817	−	7.41000i	0.168977	−	0.292677i	−0.769083	−	0.639149i	$-0.779287\pi$
$641$	4.27817	−	7.41000i	0.168977	−	0.292677i	0.938061	+	0.346471i	$0.112620\pi$
$642$		0			0
$643$	−24.2681	−	14.0112i	−0.957042	−	0.552548i	−0.0617804	−	0.998090i	$-0.519678\pi$
$643$	−24.2681	−	14.0112i	−0.957042	−	0.552548i	−0.895261	+	0.445541i	$0.853011\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$			9.57376i			0.376383i	0.982132	+	0.188192i	$0.0602626\pi$
$647$			9.57376i			0.376383i	−0.982132	+	0.188192i	$0.939737\pi$
$648$		0			0
$649$	0.0924936	−	0.160204i	0.00363069	−	0.00628854i
$650$		0			0
$651$		0			0
$652$		0			0
$653$			16.4168i			0.642439i	0.947005	+	0.321219i	$0.104093\pi$
$653$			16.4168i			0.642439i	−0.947005	+	0.321219i	$0.895907\pi$
$654$		0			0
$655$	−20.9963	−	11.6162i	−0.820394	−	0.453882i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−7.08162	−	12.2657i	−0.275861	−	0.477805i	0.694491	−	0.719501i	$-0.255629\pi$
$659$	−7.08162	−	12.2657i	−0.275861	−	0.477805i	−0.970352	+	0.241697i	$0.922296\pi$
$660$		0			0
$661$	−18.5170	−	32.0724i	−0.720229	−	1.24747i	−0.960908	−	0.276868i	$-0.910704\pi$
$661$	−18.5170	−	32.0724i	−0.720229	−	1.24747i	0.240679	−	0.970605i	$-0.422630\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−8.88717	−	9.62429i	−0.344630	−	0.373214i
$666$		0			0
$667$	14.6178	+	8.43960i	0.566004	+	0.326783i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−2.72453	−	4.71903i	−0.105179	−	0.182176i
$672$		0			0
$673$			42.3293i			1.63167i	0.578282	+	0.815837i	$0.303723\pi$
$673$			42.3293i			1.63167i	−0.578282	+	0.815837i	$0.696277\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$			13.9856i			0.537510i	0.963209	+	0.268755i	$0.0866121\pi$
$677$			13.9856i			0.537510i	−0.963209	+	0.268755i	$0.913388\pi$
$678$		0			0
$679$	0.560033	−	0.970005i	0.0214921	−	0.0372254i
$680$		0			0
$681$		0			0
$682$		0			0
$683$			11.6668i			0.446416i	0.974771	+	0.223208i	$0.0716529\pi$
$683$			11.6668i			0.446416i	−0.974771	+	0.223208i	$0.928347\pi$
$684$		0			0
$685$	−19.8106	−	32.9099i	−0.756925	−	1.25742i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	14.3273	−	24.8156i	0.545825	−	0.945397i
$690$		0			0
$691$	−15.7886			−0.600627			−0.300313	−	0.953841i	$-0.597091\pi$
$691$	−15.7886			−0.600627			−0.300313	+	0.953841i	$0.597091\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	14.0384	−	8.45062i	0.532506	−	0.320550i
$696$		0			0
$697$	6.36760	−	3.67633i	0.241190	−	0.139251i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−2.64450	+	4.58042i	−0.0998816	+	0.173000i	−0.911635	−	0.411000i	$-0.865180\pi$
$701$	−2.64450	+	4.58042i	−0.0998816	+	0.173000i	0.811754	+	0.584000i	$0.198513\pi$
$702$		0			0
$703$	18.1409	−	16.1478i	0.684198	−	0.609025i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	17.2497	−	9.95913i	0.648743	−	0.374552i
$708$		0			0
$709$	−12.2529	−	21.2226i	−0.460166	−	0.797031i	0.538803	−	0.842432i	$-0.318877\pi$
$709$	−12.2529	−	21.2226i	−0.460166	−	0.797031i	−0.998969	+	0.0454011i	$0.985543\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−3.62075	+	2.09044i	−0.135598	+	0.0782875i
$714$		0			0
$715$	−14.7619	−	24.5229i	−0.552064	−	0.917104i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−22.4239	+	38.8393i	−0.836269	+	1.44846i	0.0567236	+	0.998390i	$0.481935\pi$
$719$	−22.4239	+	38.8393i	−0.836269	+	1.44846i	−0.892993	+	0.450071i	$0.851399\pi$
$720$		0			0
$721$	12.6442			0.470896
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−5.50405	−	8.77660i	−0.204415	−	0.325955i
$726$		0			0
$727$	−28.1376	−	16.2453i	−1.04357	−	0.602504i	−0.122726	−	0.992441i	$-0.539164\pi$
$727$	−28.1376	−	16.2453i	−1.04357	−	0.602504i	−0.920842	+	0.389937i	$0.872497\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	8.65152	+	14.9849i	0.319988	+	0.554235i
$732$		0			0
$733$			11.1969i			0.413568i	0.978387	+	0.206784i	$0.0662998\pi$
$733$			11.1969i			0.413568i	−0.978387	+	0.206784i	$0.933700\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−3.49009	+	2.01501i	−0.128559	+	0.0742237i
$738$		0			0
$739$	0.466361	−	0.807761i	0.0171554	−	0.0297140i	−0.857320	−	0.514783i	$-0.827872\pi$
$739$	0.466361	−	0.807761i	0.0171554	−	0.0297140i	0.874476	+	0.485069i	$0.161206\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	23.3370	+	13.4736i	0.856153	+	0.494300i	0.862722	−	0.505678i	$-0.168758\pi$
$743$	23.3370	+	13.4736i	0.856153	+	0.494300i	−0.00656939	+	0.999978i	$0.502091\pi$
$744$		0			0
$745$	−23.9601	−	13.2559i	−0.877829	−	0.485658i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−17.2210			−0.629240
$750$		0			0
$751$	2.33645	+	4.04686i	0.0852584	+	0.147672i	0.905501	−	0.424343i	$-0.139495\pi$
$751$	2.33645	+	4.04686i	0.0852584	+	0.147672i	−0.820243	+	0.572015i	$0.806162\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	0.471994	+	25.8394i	0.0171776	+	0.940392i
$756$		0			0
$757$	37.0902	+	21.4140i	1.34807	+	0.778306i	0.987975	−	0.154612i	$-0.0494126\pi$
$757$	37.0902	+	21.4140i	1.34807	+	0.778306i	0.360090	+	0.932918i	$0.382746\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	16.7169			0.605987			0.302994	−	0.952993i	$-0.402014\pi$
$761$	16.7169			0.605987			0.302994	+	0.952993i	$0.402014\pi$
$762$		0			0
$763$	−2.32065	−	1.33983i	−0.0840131	−	0.0485050i
$764$		0			0
$765$		0			0
$766$		0			0
$767$		−	0.0857182i		−	0.00309511i
$768$		0			0
$769$	−7.70852	−	13.3516i	−0.277976	−	0.481469i	0.692905	−	0.721029i	$-0.256330\pi$
$769$	−7.70852	−	13.3516i	−0.277976	−	0.481469i	−0.970882	+	0.239559i	$0.922997\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−28.7343	+	16.5897i	−1.03350	+	0.596691i	−0.917985	−	0.396615i	$-0.870185\pi$
$773$	−28.7343	+	16.5897i	−1.03350	+	0.596691i	−0.115514	+	0.993306i	$0.536852\pi$
$774$		0			0
$775$	2.56432	−	0.0937133i	0.0921132	−	0.00336628i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−23.0813	+	4.76868i	−0.826975	+	0.170856i
$780$		0			0
$781$	29.8774	−	51.7491i	1.06910	−	1.85173i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	4.48139	−	8.10014i	0.159948	−	0.289106i
$786$		0			0
$787$		−	12.8318i		−	0.457405i	−0.973496	−	0.228702i	$-0.926552\pi$
$787$		−	12.8318i		−	0.457405i	0.973496	−	0.228702i	$-0.0734483\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	11.2179			0.398862
$792$		0			0
$793$	−2.18667	−	1.26248i	−0.0776511	−	0.0448319i
$794$		0			0
$795$		0			0
$796$		0			0
$797$			2.28485i			0.0809336i	0.999181	+	0.0404668i	$0.0128845\pi$
$797$			2.28485i			0.0809336i	−0.999181	+	0.0404668i	$0.987115\pi$
$798$		0			0
$799$	4.44028			0.157086
$800$		0			0
$801$		0			0
$802$		0			0
$803$	9.79861	+	5.65723i	0.345786	+	0.199639i
$804$		0			0
$805$	−20.9759	+	12.6268i	−0.739305	+	0.445036i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	17.3304			0.609305			0.304652	−	0.952464i	$-0.401460\pi$
$809$	17.3304			0.609305			0.304652	+	0.952464i	$0.401460\pi$
$810$		0			0
$811$	−24.7926	−	42.9420i	−0.870586	−	1.50790i	−0.861392	−	0.507941i	$-0.830407\pi$
$811$	−24.7926	−	42.9420i	−0.870586	−	1.50790i	−0.00919378	−	0.999958i	$-0.502927\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	21.0529	−	0.384562i	0.737452	−	0.0134706i
$816$		0			0
$817$	−11.2221	−	54.3173i	−0.392612	−	1.90032i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	11.1029	+	19.2308i	0.387495	+	0.671160i	0.992112	−	0.125356i	$-0.0400073\pi$
$821$	11.1029	+	19.2308i	0.387495	+	0.671160i	−0.604617	+	0.796516i	$0.706674\pi$
$822$		0			0
$823$	−16.5674	+	9.56519i	−0.577503	+	0.333422i	−0.760141	−	0.649759i	$-0.774870\pi$
$823$	−16.5674	+	9.56519i	−0.577503	+	0.333422i	0.182637	+	0.983180i	$0.441537\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−13.0330	+	7.52461i	−0.453202	+	0.261656i	−0.709182	−	0.705026i	$-0.750935\pi$
$827$	−13.0330	+	7.52461i	−0.453202	+	0.261656i	0.255980	+	0.966682i	$0.417602\pi$
$828$		0			0
$829$	−3.62995			−0.126074			−0.0630368	−	0.998011i	$-0.520079\pi$
$829$	−3.62995			−0.126074			−0.0630368	+	0.998011i	$0.520079\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−6.11621	−	3.53120i	−0.211914	−	0.122349i
$834$		0			0
$835$	15.7656	+	26.1903i	0.545592	+	0.906351i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	9.47453	−	16.4104i	0.327097	−	0.566549i	−0.654838	−	0.755770i	$-0.727263\pi$
$839$	9.47453	−	16.4104i	0.327097	−	0.566549i	0.981935	+	0.189221i	$0.0605963\pi$
$840$		0			0
$841$	12.3535	−	21.3969i	0.425984	−	0.737826i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	13.8302	+	7.65152i	0.475772	+	0.263220i
$846$		0			0
$847$		−	22.3443i		−	0.767761i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−22.6954	−	39.3095i	−0.777987	−	1.34751i
$852$		0			0
$853$	37.0287	+	21.3785i	1.26784	+	0.731987i	0.974579	−	0.224045i	$-0.0719264\pi$
$853$	37.0287	+	21.3785i	1.26784	+	0.731987i	0.293260	+	0.956033i	$0.405260\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	2.71973	+	1.57024i	0.0929043	+	0.0536383i	0.545732	−	0.837960i	$-0.316252\pi$
$857$	2.71973	+	1.57024i	0.0929043	+	0.0536383i	−0.452828	+	0.891598i	$0.649585\pi$
$858$		0			0
$859$	3.53437	+	6.12170i	0.120591	+	0.208870i	0.920001	−	0.391916i	$-0.128188\pi$
$859$	3.53437	+	6.12170i	0.120591	+	0.208870i	−0.799410	+	0.600786i	$0.794854\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		−	0.464328i		−	0.0158059i	−0.999969	−	0.00790296i	$-0.997484\pi$
$863$		−	0.464328i		−	0.0158059i	0.999969	−	0.00790296i	$-0.00251562\pi$
$864$		0			0
$865$	12.7493	−	23.0443i	0.433488	−	0.783531i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	34.0888	−	59.0435i	1.15638	−	2.00291i
$870$		0			0
$871$	−0.933701	+	1.61722i	−0.0316373	+	0.0547973i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	15.0041	−	0.822948i	0.507232	−	0.0278207i
$876$		0			0
$877$	0.802896	+	0.463552i	0.0271119	+	0.0156530i	0.513495	−	0.858093i	$-0.328351\pi$
$877$	0.802896	+	0.463552i	0.0271119	+	0.0156530i	−0.486383	+	0.873746i	$0.661684\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−4.50850			−0.151895			−0.0759477	−	0.997112i	$-0.524198\pi$
$881$	−4.50850			−0.151895			−0.0759477	+	0.997112i	$0.524198\pi$
$882$		0			0
$883$	29.6605	−	17.1245i	0.998156	−	0.576286i	0.0904542	−	0.995901i	$-0.471168\pi$
$883$	29.6605	−	17.1245i	0.998156	−	0.576286i	0.907702	+	0.419615i	$0.137835\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	24.7321	−	14.2791i	0.830423	−	0.479445i	−0.0235747	−	0.999722i	$-0.507505\pi$
$887$	24.7321	−	14.2791i	0.830423	−	0.479445i	0.853997	+	0.520277i	$0.174171\pi$
$888$		0			0
$889$	13.8310	+	23.9560i	0.463876	+	0.803457i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−13.5113	−	4.47544i	−0.452138	−	0.149765i
$894$		0			0
$895$	0.676798	+	37.0515i	0.0226229	+	1.23849i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−0.531667	−	0.920874i	−0.0177321	−	0.0307129i
$900$		0			0
$901$	15.9991			0.533007
$902$		0			0
$903$		0			0
$904$		0			0
$905$	27.5696	−	16.5960i	0.916445	−	0.551668i
$906$		0			0
$907$	13.6098	+	7.85765i	0.451907	+	0.260909i	0.708635	−	0.705575i	$-0.249311\pi$
$907$	13.6098	+	7.85765i	0.451907	+	0.260909i	−0.256728	+	0.966484i	$0.582644\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−20.7125			−0.686237			−0.343119	−	0.939292i	$-0.611483\pi$
$911$	−20.7125			−0.686237			−0.343119	+	0.939292i	$0.611483\pi$
$912$		0			0
$913$		−	22.0909i		−	0.731103i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−12.4906	−	7.21143i	−0.412475	−	0.238142i
$918$		0			0
$919$	−30.6628			−1.01147			−0.505737	−	0.862688i	$-0.668779\pi$
$919$	−30.6628			−1.01147			−0.505737	+	0.862688i	$0.668779\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$		−	27.6888i		−	0.911388i
$924$		0			0
$925$	1.01742	+	27.8402i	0.0334526	+	0.915380i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	7.65011	−	13.2504i	0.250992	−	0.434731i	−0.712807	−	0.701360i	$-0.752577\pi$
$929$	7.65011	−	13.2504i	0.250992	−	0.434731i	0.963799	+	0.266629i	$0.0859099\pi$
$930$		0			0
$931$	15.0518	+	16.9097i	0.493303	+	0.554193i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	7.73669	−	13.9841i	0.253017	−	0.457329i
$936$		0			0
$937$	3.83862	−	2.21623i	0.125402	−	0.0724011i	−0.435987	−	0.899953i	$-0.643601\pi$
$937$	3.83862	−	2.21623i	0.125402	−	0.0724011i	0.561389	+	0.827552i	$0.310267\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	17.3400	+	30.0338i	0.565268	+	0.979073i	0.997025	+	0.0770825i	$0.0245605\pi$
$941$	17.3400	+	30.0338i	0.565268	+	0.979073i	−0.431757	+	0.901990i	$0.642106\pi$
$942$		0			0
$943$			44.0490i			1.43443i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	1.04606	+	0.603945i	0.0339925	+	0.0196256i	0.516900	−	0.856046i	$-0.327086\pi$
$947$	1.04606	+	0.603945i	0.0339925	+	0.0196256i	−0.482907	+	0.875671i	$0.660419\pi$
$948$		0			0
$949$	5.24283			0.170189
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−51.3773	−	29.6627i	−1.66427	−	0.960868i	−0.970639	−	0.240540i	$-0.922676\pi$
$953$	−51.3773	−	29.6627i	−1.66427	−	0.960868i	−0.693633	−	0.720329i	$-0.743991\pi$
$954$		0			0
$955$	−0.243873	−	13.3509i	−0.00789156	−	0.432025i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−11.5443	−	19.9952i	−0.372784	−	0.645680i
$960$		0			0
$961$	−30.7366			−0.991504
$962$		0			0
$963$		0			0
$964$		0			0
$965$	17.6300	−	31.8662i	0.567528	−	1.02581i
$966$		0			0
$967$	39.4450	+	22.7736i	1.26847	+	0.732350i	0.974698	−	0.223527i	$-0.0717570\pi$
$967$	39.4450	+	22.7736i	1.26847	+	0.732350i	0.293769	+	0.955876i	$0.405090\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	0.738715	−	1.27949i	0.0237065	−	0.0410608i	−0.853929	−	0.520390i	$-0.825787\pi$
$971$	0.738715	−	1.27949i	0.0237065	−	0.0410608i	0.877635	+	0.479329i	$0.159120\pi$
$972$		0			0
$973$	8.52937	−	4.92443i	0.273439	−	0.157870i
$974$		0			0
$975$		0			0
$976$		0			0
$977$			46.8443i			1.49868i	0.662184	+	0.749341i	$0.269630\pi$
$977$			46.8443i			1.49868i	−0.662184	+	0.749341i	$0.730370\pi$
$978$		0			0
$979$	−19.2066	−	33.2668i	−0.613846	−	1.06321i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−17.4012	−	10.0466i	−0.555011	−	0.320436i	0.196130	−	0.980578i	$-0.437163\pi$
$983$	−17.4012	−	10.0466i	−0.555011	−	0.320436i	−0.751141	+	0.660142i	$0.770496\pi$
$984$		0			0
$985$	−25.7625	+	0.470589i	−0.820861	+	0.0149942i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−103.660			−3.29621
$990$		0			0
$991$	−8.95274	+	15.5066i	−0.284393	+	0.492583i	−0.972462	−	0.233062i	$-0.925125\pi$
$991$	−8.95274	+	15.5066i	−0.284393	+	0.492583i	0.688069	+	0.725646i	$0.258459\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	18.3890	−	11.0695i	0.582971	−	0.350928i
$996$		0			0
$997$	1.71445	−	0.989838i	0.0542972	−	0.0313485i	−0.472606	−	0.881274i	$-0.656686\pi$
$997$	1.71445	−	0.989838i	0.0542972	−	0.0313485i	0.526903	+	0.849926i	$0.323353\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3420.2.bj.c.1189.6		20
3.2	odd	2		380.2.r.a.49.8	yes	20
5.4	even	2	inner	3420.2.bj.c.1189.8		20
15.2	even	4		1900.2.i.g.201.8		20
15.8	even	4		1900.2.i.g.201.3		20
15.14	odd	2		380.2.r.a.49.3	✓	20
19.7	even	3	inner	3420.2.bj.c.2629.8		20
57.26	odd	6		380.2.r.a.349.3	yes	20
95.64	even	6	inner	3420.2.bj.c.2629.6		20
285.83	even	12		1900.2.i.g.501.3		20
285.197	even	12		1900.2.i.g.501.8		20
285.254	odd	6		380.2.r.a.349.8	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.2.r.a.49.3	✓	20	15.14	odd	2
380.2.r.a.49.8	yes	20	3.2	odd	2
380.2.r.a.349.3	yes	20	57.26	odd	6
380.2.r.a.349.8	yes	20	285.254	odd	6
1900.2.i.g.201.3		20	15.8	even	4
1900.2.i.g.201.8		20	15.2	even	4
1900.2.i.g.501.3		20	285.83	even	12
1900.2.i.g.501.8		20	285.197	even	12
3420.2.bj.c.1189.6		20	1.1	even	1	trivial
3420.2.bj.c.1189.8		20	5.4	even	2	inner
3420.2.bj.c.2629.6		20	95.64	even	6	inner
3420.2.bj.c.2629.8		20	19.7	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 3420 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3420.bj (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0408382 - 2.23570i) q^{5} -1.34403i q^{7} -5.25594 q^{11} +(-2.10918 + 1.21773i) q^{13} +(-1.17765 - 0.679914i) q^{17} +(2.89815 + 3.25587i) q^{19} +(7.05514 - 4.07329i) q^{23} +(-4.99666 + 0.182603i) q^{25} +(1.03597 + 1.79435i) q^{29} -0.513207 q^{31} +(-3.00483 + 0.0548876i) q^{35} -5.57175i q^{37} +(-2.70353 + 4.68265i) q^{41} +(-11.0197 - 6.36221i) q^{43} +(-2.82785 + 1.63266i) q^{47} +5.19359 q^{49} +(-10.1892 + 5.88276i) q^{53} +(0.214643 + 11.7507i) q^{55} +(-0.0175979 + 0.0304805i) q^{59} +(0.518372 + 0.897846i) q^{61} +(2.80861 + 4.66574i) q^{65} +(0.664028 - 0.383377i) q^{67} +(-5.68450 + 9.84583i) q^{71} +(-1.86429 - 1.07635i) q^{73} +7.06413i q^{77} +(-6.48576 + 11.2337i) q^{79} +4.20304i q^{83} +(-1.47199 + 2.66062i) q^{85} +(3.65426 + 6.32937i) q^{89} +(1.63667 + 2.83479i) q^{91} +(7.16079 - 6.61235i) q^{95} +(0.721716 + 0.416683i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - q^{5} + 14 q^{19} + 9 q^{25} + 16 q^{29} + 8 q^{31} + 2 q^{35} - 26 q^{41} - 44 q^{49} - 12 q^{55} - 4 q^{59} + 2 q^{61} + 18 q^{65} + 2 q^{71} - 16 q^{79} - 39 q^{85} + 40 q^{89} - 4 q^{91} + 43 q^{95}+O(q^{100}) \) 20 * q - q^5 + 14 * q^19 + 9 * q^25 + 16 * q^29 + 8 * q^31 + 2 * q^35 - 26 * q^41 - 44 * q^49 - 12 * q^55 - 4 * q^59 + 2 * q^61 + 18 * q^65 + 2 * q^71 - 16 * q^79 - 39 * q^85 + 40 * q^89 - 4 * q^91 + 43 * q^95

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